Knockback happens when you get hit by something big and blunt that sends you flying instead of just doing damage to you. If you make a blunt attack with Super Strength, and it inflicts damage equal to your greater than your target’s Knockback Threshold, then that target is Knocked Back. Unless you have the Light Knockback feat, you provoke Knockback whether you want to or not. Your Knockback Threshold is a fairly simply formula:
10 + Strength modifier + Fortitude save + size modifier
GMs might rule that a slashing attack with a particularly large weapon, such as an over-sized axe, might provoke Knockback.
If you are Knocked Back, you take damage normally, but you are also thrown directly away from your attacker for a number of squares equal to one tenth (1/10th) the damage of the attack (i.e., half the damage, in feet) and you fall. If the damage is less than 10, then you are only Knocked Back within your square, but you still fall.
If you roll a Reflex save (DC 15), then you land on your feet, or kip up, or do something equally cool. If you can fly or otherwise control your position in space, then your Reflex Save is only 10, and you halve the distance to which you are Knocked Back.
If you have DR, then take that amount off of the damage before you calculate your Knockback distance. You incur attacks of opportunity while you sail through the air in this manner.
If you get Knocked Back from a direction other than laterally, then different things happen because of gravity. From above, double the distance; from below, halve the distance.
Size modifiers apply to your Knockback Threshold, as above, and they also apply to your damage roll for the purposes of provoking Knockback, but it doesn’t increase the actual damage.
If you pass through someone else’s square when you’re Knocked Back, then they must roll a Reflex Save (DC 15) to avoid being hit by you. If they fail, you slam into them and you roll 1d6 for every square you had left to travel. The two of you split that damage and must make another Reflex save (DC 15) to avoid falling in a heap (as above). This is called Cascading Knockback. A GM who likes math could have you continue to cause Knockback as you fly through the air, but it’s a lot of finicky numbers and there are only so many hours in the day. If you simply hit a wall or other fixed object during your Knockback, don’t bother with the first Reflex save. You and the wall share the damage; don’t forget that the wall could have Hardness.
If you provoke knockback as part of an iterative attack, you make your full attack regardless of where in the sequence the knockback occurred, and you calculate using the highest damage roll (i.e., the distance doesn’t stack).